Guaranteed cost coherent control for quantum systems with non-quadratic perturbations in the system Hamiltonian

This paper considers a class of uncertain quantum systems subject to non-quadratic perturbations in the system Hamiltonian. Results on performance analysis for this class of systems are presented using a linear matrix inequality method. Guaranteed cost coherent controllers are designed through adding a controller Hamiltonian to the quantum systems. A numerical procedure is proposed for the controller synthesis to deal with a non-convex problem in the design process. An example of a quantum system comprised of a Josephson junction coupled to an electromagnetic resonant cavity is presented to illustrate the control method.